When I have a monitor plugged in at work (dual monitor) and I go to About this Mac -> More Info it says Graphics Radeon HD6770. But when I unplug the monitor and just use the laptop display (17") It says Intel graphics. Is this normal? This is a brand new machine.
Yes this is normal. Both the 15" and the 17" MacBook Pro have two graphic cards and use the Intel HD graphics for normal function and switch to the ATI Radeon when a more graphically demanding application is being run. Also when you connect the external display the ATI card kicks in in order to drive both of your screens. This is why you get the blue screen flash when you connect and disconnect an external monitor (the graphics source is being switched)
Yes, this is exactly how it is supposed to work. The MBP models have both a discrete and integrated graphics card. You can even disable or enable the Automatic graphics switching in System Prefs - Energy saver - Automatic graphics switching.